Just some clarification here: State and Federal criminal law apply on reservations. All people in the US have the same rights in criminal courts. A tribal court will sometimes hear criminal cases that only involve tribal members, if all parties agree. This issue came up in the case involving the UAW and Foxwoods, where a judge ruled than an American Indian or an employee of a reservation has the same right to join a union as any other person in America. It is a myth that you can be beaten, raped or kidnapped on a reservation with no consequences under US law. Indian casinos exist because the federal law supersedes state laws and the tribes received permission from the US to build casinos, being there is no federal law against casino gaming. States may not negotiate or sign treaties with tribes, but states with tribal casinos have received federal permission to engage in compacts to work out the details like road-building and taxes remitted to the state.
State and Federal civil law do not apply on reservations in cases between the tribe and civilians because the tribes are said to have sovereign immunity just like any other government. If you fall down the stairs in an IJ you won't be able to sue the casino for negligence. If another patron assaults you, you will have criminal and civil recourse against that person. If a casino security guard assaults you, you will have criminal and civil recourse against the guard as an individual, but any judgment may be hard to collect if he has no assets or employment outside the reservation. If the casino decides not to pay you your winnings, you will have no recourse in state court but you may get some relief under Federal law. Unlikely, because these laws haven't been tested yet, but no casino wants to be the test case for this so they will probably just pay you rather than get the bad press.